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all roots in (-inf, 0]"}]}],"used_by":[],"used_by_total":0,"links":[],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n 0: 1;\n 1: 46, 56, 16;\n 2: 2116, 5152, 4608, 1792, 256;\n 3: 97336, 355488, 534336, 422912, 185856, 43008, 4096;\n 4: 4477456, 21803264, 46044160, 55064576, 40781824, 19152896, 5570560, 917504, 65536;\n 5: 205962976, 1253687680, 3410653440, 5460295680, 5696286720, 4045848576, 1981317120, 660602880, 143523840, 18350080, 1048576;\n 6: 9474296896, 69203559936, 230391975936, 462229196800, 622376202240, 592465821696, 408848695296, 206075068416, 75296931840, 19451084800, 3372220416, 352321536, 16777216;\n 7: 435817657216, 3713924383232, 14625018999808, 35271750664192, 58200411938816, 69502162272256, 61943145234432, 41854433230848, 21545441820672, 8408579178496, 2449133797376, 516268490752, 74457284608, 6576668672, 268435456;\n 8: 20047612231936, 195246310432768, 887703721967616, 2500924384673792, 4886437290377216, 7020670543724544, 7672712359051264, 6506154658103296, 4326028908429312, 2263010315862016, 928267657805824, 295437110083584, 71522211332096, 12732430548992, 1571958030336, 120259084288, 4294967296;\n 9: 922190162669056, 10103996564895744, 52088926390456320, 167877871092105216, 379031140450566144, 636606123427233792, 824285315610968064, 841285735079215104, 686105388386353152, 450454567931346944, 238645352482209792, 101781260954763264, 34686782410850304, 9317929401188352, 1929681561452544, 297280456359936, 32083405701120, 2164663517184, 68719476736;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (46+56*x+16*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(46 + 56*x + 16*x^2)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (46 + 56*x + 16*x^2)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-d3c3090977105807","steps":["basis A013611","x \u21a6 x+1"],"edges":["e-bced44278fba7ed1","e-1fa65ef038e158a8"],"text":"A272867 \u2192 basis A013611 \u2192 x \u21a6 x+1"},"headline":"A272867 \u2192 basis A013611 \u2192 x \u21a6 x+1","chain":null}